admits a unique solution \((\widetilde{\eta }(t,\cdot ),\widetilde{\zeta }(t,\cdot ))\in L^\infty _\mathbb {F}(\Omega ;C([t,T];\mathbb {R}^n))\times \overline{{\rm BMO}}([t,T];\mathbb {R}^n)\)  (see Proposition REF  or [1]}). By (REF ) and (REF ), it is immediate that for \({\rm a.e.}\ t\in [0,T]\) ,
\(\widetilde{Y}(t)=\mathbb {E}_t\Big [\psi (t)+\int _t^Tg(t,s,y(s),\widetilde{Z}(t,s))ds\Big ]=\widetilde{\eta }(t,t)\) 
